One of the signs of a good sharpener is that the results are CONSISTENT. I'm not convinced by your description that he qualifies. I'm not sure that the wrong wheel would produce the inconsistent results you describe. Though if he uses a really coarse grain wheel, so he can sharpen blades faster, that might lead to somewhat inconsistent results, as well as very dull edges.
I wonder if, without the right jig, he is trying to level and/or center the blade on the wheel by hand. A really good tech can do that, using hand or power tools, but you need better hand-eye coordination than I personally possess.
If the sharpener is GOOD, and doesn't remove much metal / sharpening, a blade will last about 30 sharpenings, more or less. (Assume a good sharpener using power tools removes .003 inches of steel. Assume the relationship of your toe pick to the rest of your blade is messed up after .1 inches are removed.) So -- drop 3 sharpenings off the lifetime, and see how much the bad attempts cost you in terms of replacing blades - you are paying for more than lost ice time. E.g., if your blades cost $300-$500 per pair, each sharpening costs you at least $10-$16.67 more per pair than you think, maybe several times that. Add in lost ice time, wasted lessons, and he is costing you a lot. If you actually drive to his shop, that costs you more too.
If he isn't very good, he is probably removing more metal, maybe several times as much or more, and you may be paying even more for his sharpenings, indirectly. If there is another nearby tech within a few hours drive, it is likely worth it. Dubious techs also frequently modify the rocker profile (the longitudinal edge curvatures) in unpredictable ways, leaving you with a blade that can be very difficult to skate on. For example, new blades have one or more transition points up front, near the ball of your foot, between different rocker curvatures. You typically balance on or near that point, especially when turning or spinning. But if the tech smooths out the transition, or moves it, you can't feel where it is anymore, and you may rock around different parts of the blade. A really, really bad tech may remove part of your toe pick, and if he does that badly enough, you may as well throw away the blade.
Amazingly, some skaters van learn to skate on slightly uneven blade edges. But if the tilt goes back and forth along the blade, that gets really hard to correct for.
Another possibility: are either of your blades warped? E.g., if you put a straight edge along the side of the blade, can you see a gap anywhere? A second rate skate tech using a power sharpener, especially one without the proper blade holder, will produces edges that tilt one way at the ends, and another in the middle, or some other such uneven pattern.
Very sharp blades are BTW very easy to have misaligned, in terms of the fact that the edges might not point straight down. In particular, sometimes the edges are pushed off to the sides by sharpening - forming a "lip" or "burr".
If you want to feel the edges, to see how they point, touch them very lightly. I do not recommend drawing your finger ALONG the edge, as it is quite easy to cut yourself that way. I draw my finger ACROSS the edge, very, very lightly. If you do cut yourself (I don't, anymore), wash the cut clean, and bandage - you don't want an infection.
You can point the edges correctly, or deburr them (deburring means deliberately making them less sharp, but the ultrasharp pointed foil edges I prefer are more fragile), using a number of techniques. I take a small very fine grain flat sharpening stone, and brush the edge from the side upwards. In fact, half the time or more, that will work just as well as re-sharpening the edges, because a lot of the time non-sharp edges have just been bent. The technique is a little harder for edges that are bent inwards, but if you are careful, you can do it.
The usual technique is not to slide the stone along the sides - which scratches them up, and
possibly therefore slows down the blades - but to bend them very slightly inwards.
There are a lot of Youtube videos demonstrating this type of thing.
tsop4me says he prefers using a "steel" to straighten edges. I haven't tried that. I like the fine flat stone partly because it also polishes the edge to make the edge more clean, but in theory, a steel might mean you would need to fully sharpen even less often.
Have you asked other skaters what they are doing about this bad tech? I assume they are having problems too. Maybe they have found someone they like, and you can carpool, or alternate who takes a group of skates with them to the distant tech.
I personally love sharpening myself using good purpose-built hand tools, like the
Pro-Filer, but I admit it takes time to learn to DIY. It costs about $80 and is only available for 3/8" and 1/2", which is high - but compared to the costs I just cited, it isn't so bad. I try to remove no more than about .001 inches / sharpening - but if your dubious skate tech has made the edges uneven, or made them very dull, you will need to remove more to correct things the first time. If you do it right, you can substantially increase the lifetime of your blades relative to sharpening with power tools, especially if your tech is incompetent - but of course, you can do it wrong. E.g., it is really important you trace or otherwise record the original rocker profile, so you don't lose it. I also like to cover the toe picks with tape first, so I can't destroy them.
Buying your own power sharpening tool, like Bill did, is a pretty expensive route, if you are only doing your own blades. And that has an even bigger learning curve, because metal comes off so fast. Also, it won't fit in your skate bag. I personally haven't done it.